A summation theorem for hypergeometric series very-well poised on G 2
A summation theorem for hypergeometric series very-well poised on G 2
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DOI：
10.1137/0521027
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发表时间：
1990-03
影响因子：
2
通讯作者：
R. A. Gustafson
中科院分区：
文献类型：
--
作者：
R. A. Gustafson
对于李代数$G_2 $上非常稳定的基本超几何级数，证明了Bailey的${}_6 \psi _6 $求和定理的一个类比。作为一种极限情况，得到了一类$G_2 $仿射根的Macdonald恒等式的一个新的证明。用卡尔森定理证明了在$G_2 $上很好定态的普通超几何级数的一个求和定理。
An analogue of Bailey’s ${}_6 \psi _6 $ summation theorem is proved for basic hypergeometric series that are very well poised on the Lie algebra $G_2 $. As a limiting case, a new proof of the Macdonald identity associated to the affine root system of type $G_2 $ is obtained. A summation theorem for ordinary hypergeometric series that are very well poised on $G_2 $ is proved by Carlson’s theorem.